Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree

Fuente: arXiv
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Main Authors: Montero, Antonio, Potočnik, Primož
Format: Preprint
Published: 2024
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author Montero, Antonio
Potočnik, Primož
author_facet Montero, Antonio
Potočnik, Primož
contents The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results we classify vertex-transitive graphs whose motion is $4$ or a prime number.
format Preprint
id arxiv_https___arxiv_org_abs_2405_10088
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
Montero, Antonio
Potočnik, Primož
Combinatorics
Primary:05C25. Secondary: 20B25, 20B10
The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results we classify vertex-transitive graphs whose motion is $4$ or a prime number.
title Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
topic Combinatorics
Primary:05C25. Secondary: 20B25, 20B10
url https://arxiv.org/abs/2405.10088